A particle of mass m is acted on by a harmonic force with potential energy function V(x) = mω²x²/2 (a one dimensional simple harmonic oscillator). If there is a wall at x = 0 so that V = ∞ for x < 0, then the energy levels are equals to
A. 0, ħω, 2ħω, ...
B. 0, ¹⁄₂ħω, ħω, ...
C. ¹⁄₂ħω, ³⁄₂ħω, ⁵⁄₂ħω, ...
D. ³⁄₂ħω, ⁷⁄₂ħω, ¹¹⁄₂ħω, ...
E. 0, ³⁄₂ħω, ⁵⁄₂ħω, ...
(GR9677 #98)
SolutionThe probability distributions for the quantum states of the oscillator without the barrier.
Infinite barrier at the origin means a node at origin, or the wave function goes to zero at x = 0.
By symmetry, the ground state will disappear, as well all the even states. Odd values remain.
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